Search

This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters' departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters' unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters' individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly. [ABSTRACT FROM AUTHOR]

This paper investigates a new cash transportation problem, which is a variant of the capacitated vehicle routing problem. To better satisfy the demands of customers (e.g., banks, large retailers, shopping centers, automated teller machines, etc.), the combination of different cash denominations (i.e., $100, $50, $20, etc.) is considered. The robbery risk, which is measured by both the amount of cash being carried and the distance covered by the vehicle carrying the cash, is limited by a risk threshold. The problem is formulated as mixed‐integer linear programming to minimize the total cost, which consists of the total travel cost and the total penalties due to the unmet expected demand of customers. A combined hybrid tabu search metaheuristic is proposed to solve this problem. Tabu search is adopted for determining routing decisions while three methods, namely the exact method, the greedy method, and the mixed method, are proposed to be embedded within the tabu search to determine the denomination combination strategy. The numerical studies show that the proposed method makes a good tradeoff between the solution quality and the computation time. Experimental results also reveal the effects of the unit penalty and the risk threshold. [ABSTRACT FROM AUTHOR]

This article proposes a nonlinear complementarity problem (NCP) formulation for the risk-aversive stochastic transit assignment problem in which in-vehicle travel time, waiting time, capacity, and the effect of congestion are considered as stochastic variables simultaneously and both their means and variances are incorporated into the formulation. A new congestion model is developed and captured in the proposed NCP formulation to account for different effects of on-board passengers and passengers waiting at stops. A reliability-based user equilibrium condition is also defined based on the proposed generalized concept of travel time budget referred to as effective travel cost, and is captured in the formulation. A column generation based algorithm is proposed to solve the NCP formulation. A survey was conducted to validate that the degree of risk aversion of transit passengers affects their route choices. Numerical studies were performed to demonstrate the problem and the effectiveness of the proposed algorithm. The results obtained show that underestimating the congestion effect and ignoring the risk aversion behavior can overestimate the patronage of transit service, which have profound implications on the profit of the operators involved and the development of transit network design models. [ABSTRACT FROM AUTHOR]